Fractional Navier–Stokes equations and a Hölder-type inequality in a sum of singular spaces

Publication year: 2011
Source: Nonlinear Analysis: Theory, Methods & Applications, In Press, Corrected Proof, Available online 14 June 2011

Lucas C.F., Ferreira , Elder J., Villamizar-Roa

In this paper we study the local well-posedness of the fractional Navier–Stokes system with initial data belonging to a sum of two pseudomeasure-type spaces denoted by PMa,b:=PMa+PMb. The proof requires showing a Hölder-type inequality in PMa,b, as well as establishing estimates of the semigroup generated by the fractional power of Laplacian (−Δ)γ on these spaces.